Mines Nancy - 3rd Year - Master 2 - Department Energy & Fluid Mechanics

Academic Year 2017-2018

Advanced Fluid Mechanics

Transition to turbulence & turbulence - Applications to thermoconvection, aerodynamics & wind energy

Syllabus       ARCHE Page


      This module is given by E. Plaut (EP) and J. Peinke (JP).

Find here a complete version of our lecture notes.

Hereafter we give the planning and a few information.

During the sessions, and during the examination, we use Mathematica (or Matlab) : bring your laptop with Mathematica (or Matlab).

Find here a collection of texts of past exams and of the exam of this year, with elements of solution.

Nous remercions la Fondation Mines Nancy et le programme Erasmus+ pour leur soutien, qui nous permet d'inviter J. Peinke à donner 3 sessions dans ce module, ainsi qu'une conférence générale.

S1 December 18, 2017 (EP)

    Natural thermoconvection, Rayleigh - Bénard thermoconvection: linear stability analysis with slip boundary conditions

    [ essential of the video presentation ]

Personal homework 1 due by January 8, 2018 (EP)

     At the very beginning of session 2 on Monday, January 8, give me an hand-written personal solution of exercise 1.1.
Scoring scale: Q. 1: 4 P ; Q. 2: 6 P ; 1 P of bonus if you use good english.
Vous avez le droit de rédiger en français...

S2 January 8, 2018 (EP)

    Rayleigh - Bénard thermoconvection with slip boundary conditions: linear and weakly nonlinear stability analysis

    Preparation of session 2:

  1. (compulsory) activate or reactivate your Mathematica (or Matlab) licence on your laptop;
  2. (optional) write for yourself the complete solution of Ex. 1.0, including the plots of the figures 1.3 and 1.4; you should realize them with Mathematica using the ContourPlot command...

    [ essential of the video presentation ]

S3 January 12 (EP)

    Rayleigh - Bénard thermoconvection: weakly nonlinear analysis, supercritical bifurcation, elements on further transitions and on the case of no-slip boundary conditions; Lorenz model & chaos; confined geometry - flow reversals...

    Preparation of session 3:

  1. (compulsory) terminate exercise 1.2: at the end of session 2, we calculated the adjoint of D ; calculate the adjoint of LR , i.e., complete the equation (1.49) of the lecture notes;
  2. (optional) solve exercise 1.3.

    [ essential of the video presentation ]

Personal homework 2 due by January 19 (EP)

    Before Friday, January 19, 13:30, upload on the ARCHE Page of the module a Mathematica Notebook (or Matlab program) that solves all questions of the exercises 1.4, 1.6 and 1.7, and creates the figures 1.5a, b and c asked for. Your program should be rather short and structured, with clear notations. It should include comments to render its reading understandable, and also, once the results are displayed, comments on the physics that they traduce. I should be able to rerun the program on my computer.

S4 January 19 (EP)

    Transition in open shear flows: generalities, the case of plane Poiseuille flow

    [ essential of the video presentation ]

S5 January 22 (EP)

    Transition in plane Poiseuille flow: linear and weakly nonlinear stability analysis, Tollmienn - Schlichting waves

    Preparation of session 5: debug your code for discretizing the Orr - Sommerfeld equation (2.21) in the case of plane Poiseuille flow, and solve completely the questions 1 to 4 of exercise 2.2; we will restart at the level of question 5.

    [ essential of the video presentation ]

S6 January 24 (EP)

    Transition in plane Poiseuille flow: weakly nonlinear stability analysis, subcritical bifurcation to Tollmienn - Schlichting waves, subcritical & saddle-node bifurcations. Transition in open shear flows...

    Preparation of session 6: check that you have a code that solves completely exercise 2.2, up to the creation of the file V1.m; write a code that solves completely exercise 2.4.

    [ essential of the video presentation ]

Turbulent flow data sets

S7 February 6 (JP)

    Wind energy : conversion principles - Rotor blade aerodynamics

    [ video presentation 1: power performance theory ; 2: towards blade design ]

S8 February 7 (JP)

    Rotor blade aerodynamics - Stochastic (Langevin) power curve

    [ video presentation 1: power curve and annual energy production ; 2: Langevin power curve ]

S9 February 8 (JP)

    Wind field and Turbulence

    [ video presentation ]

General Conference by JP on Thursday February 8

Wind Energy and the Need to Understand Turbulence

Web page of the conference

Examination February 12 (EP)

    See the page collection.htm !

Emmanuel Plaut
Last modified: Wed Jul 4 17:56:44 CEST 2018